I'm a PhD student and I'm a little embarrassed to be asking for Maths help on here, but there is something I couldn't find out by googling, so I figured I'll ask here.
I have been running two sets of experiments, the first is a base line, and the second is hopefully an improvement on the first. I repeat each experiment many times and get a set of values, for example:
first = ( 2, 3, 3, 2, 4, 2 ) mean = 2.67, stddev = 0.82, 95% interval = +/- 0.65
second = (4, 5, 6, 5, 4, 5 ) mean = 4.83, stddev = 0.75, 95% interval = +/- 0.6
Now I can work out a 95% confidence interval for both sets of values. In my report I've been writing that the first experiment on average is 2.67 +/- 0.65, and the second is 4.83 +/- 0.6. Thus the second experiment produces values 1.81 (4.83/2.67) higher (and better) than the first experiment. However I do not know what the confidence intervals would be on this (1.81) value.
I had thought I could divide the intervals together for example the first min value divided by the second's min value. But I have a feeling this isn't right.
Hopefully this has explained my problem, and that someone is able to help.
P.S These are not the real values from my experiment and some I just made up, but I hopefully want to work out the confidence intervals for both discrete and continuous data.